Question

You bought 1000 shares of ABC stock on margin at the beginning of April 2012 at $4.80 per share. You deposited a 50% margin which was higher than the initial margin of 40%. The prime rate of interest was 2.5% and your broker charged 125 basis points above the prime rate on margin loan (assume simple interest rate). The stock paid a cash dividend of $0.12 per share in February and August of 2012. Your broker charged a flat fee of $7.95per trade.

1) What was your EAR if you sold the stock for $6.12 at the end of the year?

2) what was your EAR if you did not borrow from hour broker?

Answer 1

	1)	Cost of Shares=1000*$4.80	$4,800
		Amount of margin deposited	$2,400	(50%*4800)
		Amount of Loan	$2,400
		Interest rate charged by broker=2.5+1.25	3.75%
		9 months (April-December) interest	$67.50	2400*3.75%*(9/12)
		Broker Charges for two trades(buy and Sell)	$15.90	(7.95*2)
		Total amount to be paid to broker=2400+67.5+15.9	$2,483.40
		Initial Investment	$2,400
		Amount Received after 9 months=1000*$6.12	$6,120
		Dividend of August 2012=0.12*1000	$120.00
		Dividend of February will not be received by the investor
		Since Purchase was made in April 2012
		Total amount received	$6,240	(6120+120)
		Amount payable to broker	$2,483.40
		Net amount received	$3,756.60
		Effective Annual Return (EAR)=(3756/2400)-1	0.56525
		EAR	56.53%
	2)	EAR if amount is not borrowed
		Investment =1000*4.8	$4,800
		Amount Received	$6,240
		Less:Brokerage	$15.90
		Net amount received	$6,224.10	(6240-15.90)
		EAR=(6224.10/4800)-1	0.2966875
		EAR if amount is not borrowed	29.67%